4x+5=-11x(x+5)

Solution for 4x+5=-11x(x+5) equation:

4x+5=-11x(x+5)

We move all terms to the left:

4x+5-(-11x(x+5))=0


We calculate terms in parentheses: -(-11x(x+5)), so:

-11x(x+5)

We multiply parentheses

-11x^2-55x

Back to the equation:

-(-11x^2-55x)


We get rid of parentheses

11x^2+55x+4x+5=0

We add all the numbers together, and all the variables

11x^2+59x+5=0

a = 11; b = 59; c = +5;
Δ = b2-4ac
Δ = 592-4·11·5
Δ = 3261
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-\sqrt{3261}}{2*11}=\frac{-59-\sqrt{3261}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+\sqrt{3261}}{2*11}=\frac{-59+\sqrt{3261}}{22}
$